1. I'm applying class's to each line items not the entire invoice.
2. I'm not going to delete and recreate invoices that have already been closed.
3. If you want me to move our entire process to creating and adding shipping as a line items, why do you have a shipping field? It seems your giving me a work around or advising me not to use your Shipping field?
4.  

I can see in the API that the shipping field Invoice is consider a line item but I cannot set the class even from the API:

SalesItemLineDetail shippingsItemLineDetail = new SalesItemLineDetail
{
Qty = new decimal(1.0),
ClassRef = new ReferenceType()
{
Value = ShipMethodRef
},
ItemRef = new ReferenceType()
{
Value = "SHIPPING_ITEM_ID"
}
};

Line shippingLine = new Line
{
Description = "Shipping",
Amount = shippingCost,
AmountSpecified = true,
AnyIntuitObject = shippingsItemLineDetail,
DetailType = LineDetailTypeEnum.SalesItemLineDetail,
DetailTypeSpecified = true
};

lineList.Add(shippingLine);